Modelling of Patrol Routing Problem in Context with Distributed Service Networks

Abstract

Effective planning and strategic management of Distributed Service Networks (DSNs) play a vital role in enhancing operational efficiency across both public and private sectors. These networks, often characterized by dispersed nodes providing services over large geographical areas, require consistent monitoring to ensure functionality, security, and performance. In this context, the Modelling of Patrol Routing Problem in Context with Distributed Service Networks has emerged as a crucial area in operations research and mathematical optimization.The Patrol Routing Problem (PRP) focuses on designing optimal patrol routes that enable service agents or patrol units to visit a set of distributed nodes under specific constraints such as frequency, time windows, and resource limitations. The unique complexity of PRP in DSNs arises from the decentralized nature of service points and the necessity for frequent inspections or interventions. The main challenge lies in simultaneously addressing multiple issues including zoning, route optimization, allocation of patrol units, and timing, making it a multi-dimensional problem.This paper presents a detailed study on the mathematical modelling of the Patrol Routing Problem, incorporating elements such as graph theory, integer programming, and combinatorial optimization. A systematic framework is developed to optimize patrol schedules and routes based on real-time constraints and service priorities. Through this model, decision-makers can achieve enhanced zone coverage, reduced operational costs, and improved responsiveness across distributed networks.To address the computational complexity of PRP, the study also explores various algorithms and heuristics, including exact methods and metaheuristic approaches such as genetic algorithms and ant colony optimization. These tools are evaluated based on their efficiency in handling large-scale networks with dynamic service requirements.The practical implications of this research are significant, especially in areas like urban security patrolling, utility maintenance scheduling, and sensor data collection in smart infrastructure. By implementing the proposed models, organizations can enhance the reliability and efficiency of their distributed service operations.In conclusion, the modelling of the Patrol Routing Problem in the context of Distributed Service Networks offers a powerful decision-support mechanism. It enables organizations to meet the growing demands of real-time service delivery, thereby promoting sustainability, safety, and operational excellence in modern service systems.